CMAT Number Systems questions

The number of all integers n for which $$n^{2} + 96$$ is a perfect square, is

If M, A and T ate distinct positive integers such that M $$\times$$ A $$\times$$ T = 1947, then which of the following is the maximum possible value of M + A + T?

Let S(n) represents the sum of digits of a natural number n. For example, S(128)= 1 + 2 + 8 = 11. What is the value of $$S(2^{6} \times 3^{4} \times 5^{5}$$)?

If $$\frac{1}{x}$$ is a positive fraction and $$\frac{1}{y}$$ is a negative fraction then which of the following statements are true
(A) $$\frac{1}{x} + \frac{1}{y}$$ is positive
(B) $$\frac{1}{x} - \frac{1}{y}$$ is positive
(C) $$\frac{x - y}{xy}$$ is negative
(D) $$\frac{1}{xy}$$ is positive
(E) $$\frac{1}{x^2} - \frac{1}{y^2}$$ is positive
Choose the correct answer from the options given below:

The dimensions of a floor are $$18\times24$$. What is the smallest number of identical square tiles that pave the entire floor without the need to break any tile?

Arrange the following rational numbers in ascending order:
(A) $$\frac{-4}{5}$$
(B) $$\frac{-5}{12}$$
(C) $$ \frac{-7}{18}$$
(D) $$\frac{-2}{3}$$

M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is $$\frac{1}{9}^{th}$$ of M. How many such M's are possible?

Find the smallest number by which 2400 should be divided to make it a perfect cube.

The sum of two numbers is 135 and their HCF is 9. How many such pairs of numbers can be formed ?

Simplify the following: $$\frac{0.3 \times 0.3 + 0.03 \times 0.03 - 0.6 \times 0.03}{0.54}$$

The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of two numbers is 1 : 4, then the larger among two numbers is:

If one third of one-fourth of a number is 15, then three-tenth of that number is

The following table lists the marks of  seven students(rows) of a class across six subjects(columns). The Numbers in the Parenthesis indicate the maximum marks of the subject concerned. Use the data in the table to answer the question that follows :

Who is the topper of the class?

What value should come in place of question mark(?) in the following equation?

$$360\sqrt?$$ + 4500 = 19700 - 9800

$$\sqrt{188+ \sqrt{51+ \sqrt{169}}}$$ = ?